Instanton

Normally speaking, we say that a volume has three dimensions, a surface has two dimensions, a line has one dimension and a point has zero dimensions. By this reckoning, an instanton has -1 dimension.

A point, which persists through time, has one dimension more than an instanton. As soon as an instanton is there, it is gone. It is a true point in four-dimentional space-time (or, often, in higher-dimensional constructs, in the work of many theoretical physicists.)

We might suspect some gross error in dimensional analysis, of the 'off by one' kind, given the implication of a negative dimensionality according to the prevailing convention, but in fact, as Gorgonzola has indicated below, geometry itself takes no heed of temporal dimensions - though of course it may be used to represent them - all its structures and representations are static and eternal, perpetually true in Platonic heaven...

Platonism is rescued by clearly defining what we are talking about and sticking to that definition thoughout the discussion.

Now, the concept of dimension requires that we have a particular space in mind.

If we involve time in a discussion about points in space we are mentally constructing a spacetime, which is a type of four-dimensional space. "Instanton"s, which physicists call events, are 0-dimensional points in that space.

So what about a "point" that "exists through time"? Well, we have to define "existence through time". Now, our own stream of consciousness gives us a convenient way to order three-dimensional slices of our spacetime. We identify events from one slice with events from the slices that come before or after it.

In our minds, we are imposing an equivalence relation on our abstract spacetime. What we think of as a "point through time" is really one of the equivalence classes, turned into a space by our ordering.

We can talk about the spacetime itself, in which case each event is a 0-dimensional object and each "point through time" is a one-dimensional object.

We can talk about a single slice through spacetime, in which case events are still 0-dimensional points, but "time" and thus "existence through time" has no meaning.

We can discuss an identification space constructed from all of the "points through time", which revert to being our familiar 0-dimensional objects. But then, events are not elements of that space and cannot enter the discussion.

Of course, we could confuse our models with each other, and come up with a "dimension" for an event in our identification space. Unfortunately, if we do that, we stretch our definition of "space", upon which we have relied up to this point, into something we can't rely upon. So there isn't really such a thing as a "-1 dimension", since we don't have a model containing an object that might possess such a thing.